1. Field of Invention
This invention relates to computation of turbulent flow for engineering applications.
2. Prior Art
The invented near-wall eddy-viscosity formulation has been developed as an ingredient of large-eddy simulation (LES) aimed at reducing its cost for prediction of turbulent flow at high Reynolds numbers. The Reynolds number is a non-dimensional parameter characterizing the flow of a viscous fluid and is defined as Re=uL/v, where u and L are the characteristic velocity and length-scale, respectively, and v is the kinematic viscosity of the fluid.
LES resolves the large-scale structures of the flow while modeling the small-scale phenomena. This allows many of the important flow features to be captured without the expense of resolving the smaller scales, whose effects on the large scales are accounted for by sub-grid scale (SGS) models, such as the dynamic Smagorinsky model. However, LES has not yet been applied successfully to wall-bounded flows at high Reynolds numbers, because current SGS models do not properly account for the small, dynamically important features near a wall. As a consequence, these features must be resolved, resulting in the grid resolution scaling almost as expensive as the direct numerical simulation (DNS), limiting LES to low to moderate Reynolds numbers. A comprehensive description of LES framework and SGS models is given by Sagaut, P. in “Large Eddy Simulation for Incompressible Flows”, Springer Verlag, Second Edition, 2002.
In an effort to allow LES to be efficiently applied to high Reynolds number flows, many techniques have been proposed. One such technique involves the use of grids coarsened in the wall-parallel direction, while leaving the wall-normal resolution unchanged; this reduces the computational cost for at least one order of magnitude. Not all turbulent scales can be resolved with such grids and additional modeling is required. Reynolds Averaged Navier-Stokes (RANS) equations are well suited for this type of grids because only the mean wall-normal gradients must be resolved while the entire turbulence spectrum is modeled. A comprehensive description of RANS framework and RANS turbulence models is given by Wilcox, D. C. in “Turbulence Modeling for CFD”, DCW Industries, Second Edition, 1998. A well known approach in this category is detached-eddy simulation (DES) which was designed to simulate massively separated aerodynamic flows, where RANS is used in the boundary layer and LES resolves the separated region, see Strelets, M. (2001), “Detached Eddy Simulation of Massively Separated Flows”, AIAA Paper 2001-0879. However, the coupling of RANS and LES regions is not formulated in a satisfactory manner; in the pressure-driven channel this causes a significantly overpredicted mass flow rate, see Nikitin, N. V., Nicoud, F., Wasistho, B., Squires, K. D., and Spalart, P. R. (2000), “An approach to wall modeling in large-eddy simulations,” Phys. Fluids, Vol. 12 (7), pp. 1629. Another disadvantage of DES is its strong grid-dependence, where, surprisingly, the results usually worsen with refining the computational grid. In addition, DES on the wall-resolved grids does not recover the wall-resolved LES.
Another approach to reducing the computational cost of LES is wall modeling. A review of different wall models is presented in Piomelli, U., and Balaras, E. (2002), “Wall-layer models for large-eddy simulations”, Ann. Rev. Fluid Mech., Vol. 34, pp. 349-374. These models are designed to be used with coarse grids that do not resolve the wall-layer, allowing LES at a fraction of the cost when compared to wall-resolved grids. Traditional wall models provide wall stresses to the LES as boundary conditions; a successful application of that approach is not trivial—the models are complicated and their application to general codes is not straightforward, as discussed in Cabot, W. (1997), “Wall models in large eddy simulation of separated flow”, CTR Annual Research Briefs, pp. 97-106, and Wang, M., and Moin, P. (2002), “Dynamic wall modeling for large-eddy simulation of complex turbulent flows”, Phys. Fluids, Vol. 14(7), pp. 2043-2051. In addition, these wall models are usually dependent on the numerical method and the Reynolds number.